Problem # 28

We are told 1st and last terms of a 14 elemnt GP add to 7 AND the 5th term is the geometric mean of the 2nd and 14th term. Shown to the right.

The equations

... and 4 complex roots! --->

using just the positive 1

THE ANSWER

so the sequence is A = {7/2,7/2,....7/2}

Problem # 25

AP

(working forwards)

GP (working backwards)

(2 eq with variables)

solving for d in left eq and substituting into right eq:

solving for r

Note:

r =-6 is associated with d = -1.75 AND r = 3/2 is associated with d = 2.

solving for d

A = { 2, 4, 6, 9 }

OR

A = { 2, 1/4, -3/2, 9 }